PMID- 36653979
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20230119
LR  - 20230119
IS  - 1551-0018 (Electronic)
IS  - 1547-1063 (Linking)
VI  - 19
IP  - 12
DP  - 2022 Aug 17
TI  - Analysis on determining the solution of fourth-order fuzzy initial value problem 
      with Laplace operator.
PG  - 11868-11902
LID - 10.3934/mbe.2022554 [doi]
AB  - This study presents a new analytical method to extract the fuzzy solution of the 
      fuzzy initial value problem (FIVP) of fourth-order fuzzy ordinary differential 
      equations (FODEs) using the Laplace operator under the strongly generalized 
      Hukuhara differentiability (SGH-differentiability). To this end, firstly the 
      fourth-order derivative of the fuzzy valued function (FVF) according to the type 
      of the SGH-differentiability is introduced, and then the relationships between 
      the fourth-order derivative of the FVF and its Laplace transform are established. 
      Furthermore, considering the types of differentiabilities and switching points, 
      some fundamental theorems related to the Laplace transform of the fourth-order 
      derivative of the FVF are stated and proved in detail and a method to solve FIVP 
      by the fuzzy Laplace transform is presented in detail. An application of our 
      proposed method in Resistance-Inductance circuit (RL circuit) is presented. 
      Finally, FIVP's solution is graphically analyzed to visualize and support 
      theoretical results.
FAU - Akram, Muhammad
AU  - Akram M
AD  - Department of Mathematics, University of the Punjab, New Campus, Lahore, 
      Pakistan.
FAU - Ihsan, Tayyaba
AU  - Ihsan T
AD  - Department of Mathematics, University of the Punjab, New Campus, Lahore, 
      Pakistan.
FAU - Allahviranloo, Tofigh
AU  - Allahviranloo T
AD  - Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, 
      Turkey.
FAU - Al-Shamiri, Mohammed M Ali
AU  - Al-Shamiri MMA
AD  - Department of Mathematics, Faculty of Science and Arts, Muhayl Asser, King Khalid 
      University, K.S.A.
AD  - Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, 
      Yemen.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - Math Biosci Eng
JT  - Mathematical biosciences and engineering : MBE
JID - 101197794
SB  - IM
OTO - NOTNLM
OT  - Mittag-Leffler function
OT  - SGH-differentiability
OT  - fuzzy Laplace transform
OT  - fuzzy initial-value problem
OT  - fuzzy number
EDAT- 2023/01/20 06:00
MHDA- 2023/01/20 06:01
CRDT- 2023/01/19 01:00
PHST- 2023/01/19 01:00 [entrez]
PHST- 2023/01/20 06:00 [pubmed]
PHST- 2023/01/20 06:01 [medline]
AID - 10.3934/mbe.2022554 [doi]
PST - ppublish
SO  - Math Biosci Eng. 2022 Aug 17;19(12):11868-11902. doi: 10.3934/mbe.2022554.